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max2010maxim [7]
3 years ago
10

Two lines and a ray intersect at a

Mathematics
1 answer:
saveliy_v [14]3 years ago
8 0

Answer:

m<DAE = 80°

Step-by-step explanation:

Given that m<CAB = 110°,

m<DAE = (x + 4)°,

m<EAF = 30°,

m<EAF + m<DAE = m<DAF (angle addition postulate)

30° + (x + 4)° = m<DAF (substitution)

(34 + x)° = m<DAF

<DAF and <CAB are vertically opposite angles. Vertically opposite angles are said to be congruent. Therefore:

m<DAF = m<CAB

(34 + x)° = 110° (substitution)

The equation above can be used to solve for x as follows:

34 + x = 110

x = 110 - 34 (Subtracting 34 from both sides)

x = 76

m<DAE = (x + 4)°

Plug in 76, to replace x

m<DAE = 76 + 4

m<DAE = 80°

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The circumference of a circle exceeds the radius by 74 cm. Find the radius of the circle.​
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Step-by-step explanation:

Let the radius of the circle = r cm.

Then circumference of circle = 2 π r.

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Therefore, according to the question,

\sf \:2 π r = r+ 74

\sf \: =   > 2 \times  \frac{22}{7}  \times r =  r \:  + 74

\sf \: =  >  \frac{44r}{7}  -r  = 74

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work for a publishing company. The company wants to send two employees to a statistics conference. To be​ fair, the company deci
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Answer:

(a) S = {MR, MJ, MD, MC, RJ, RD, RC, JD, JC, DC}

(b) The probability that Roberto and John attend the​ conference is 0.10.

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(d) The probability that John stays​ home is 0.60.

Step-by-step explanation:

It is provided that :

Marco (<em>M</em>), Roberto (<em>R</em>), John (<em>J</em>), Dominique (<em>D</em>) and Clarice (<em>C</em>) works for the company.

The company selects two employees randomly to attend a statistics conference.

(a)

There are 5 employees from which the company has to select two employees to send to the conference.

So the total number of ways to select two employees is:

{5\choose 2}=\frac{5!}{2!(5-2)!}=\frac{5\times 4\times 3!}{2\times 3!}=10

The 10 possible samples are:

MR, MJ, MD, MC, RJ, RD, RC, JD, JC, DC

(b)

The probability of the event <em>E</em> is:

P(E)=\frac{n(E)}{N}

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n (E) = favorable outcomes

N = Total number of outcomes.

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P(RJ)=\frac{n(RJ)}{N}=\frac{1}{10}=0.10

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n (C) = {MC, RC, JC and DC} = 4

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P(C)=\frac{n(C)}{N}=\frac{4}{10}=0.40

Thus, the probability that Clarice attends the​ conference is 0.40.

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n (J') = MR, MD, MC, RD, RC, DC

Compute the probability that John stays​ home as follows:

P(J')=\frac{n(J')}{N}=\frac{6}{10}=0.60

Thus, the probability that John stays​ home is 0.60.

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